Control ENG HW_Part_29

# Control ENG HW_Part_29 - Mass of mercury = m rg Writing a...

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min 372 . 1 min 596 . 0 5 . 0 min 372 . 1 ; 1 . 0 ) 1 ( 9 . 0 ) 1 ( ) ( 94 . 0 ) 1 ( ) ( ; ) 1 ( ) ( ) 3 . 8 % 90 2 1 2 1 596 . 0 596 . 0 1 1 1 1 1 1 1 1 1 1 = = = = = = - = - = - = + = - - - - t R R thus t e e R R e R t e R t H s s R s H t t t t τ Comment : . tan ta sec , . , 2 1 2 1 k first than changes to slowly more responds ond the R R as Also quickly state steady the regains system the indicate of values Small > 8.4 Assuming the flow in the manometer to be laminar function between applied pressure P 1 and the manometer reading h. Calculate a) steady sate gain ,b) ,c) ξ . Comment on the parameters and their relation to the physical nature of this problem.

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Assumptions: Cross-sectional area =a Length of mercury in column = L Friction factor = 16/Re (laminar flow)
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Unformatted text preview: Mass of mercury = m rg Writing a force balance on the mercury Mass X acceleration = pressure force - drag force - gravitational force ) ( 2 ) ( 2 1 2 2 gh A u Af Ap dt h d AL ρ--= g p h dt dh gD dt h d g L μ 1 2 2 8 = + + At Steady state, g p h s s 1 = = g p H dt dH gD dt H d g L 1 2 2 8 = + + = [ ] g s p s H s sH gD s H s g L ) ( ) ( ) ( 8 ) ( 1 2 = + + = [ ] ) ( ) ( 1 1 3 2 2 1 s p k s H s k s k = + +...
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Control ENG HW_Part_29 - Mass of mercury = m rg Writing a...

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